Mohammad Sajid- Ph. D. (Mathematics) Indian Institute of Technology Kanpur, India
- Professor of Mathematics at Qassim University
Mohammad Sajid
- Ph. D. (Mathematics) Indian Institute of Technology Kanpur, India
- Professor of Mathematics at Qassim University
Running 3 Projects supported by Qassim Uni.;
Collaborative Research; Fellow of IMA;
Editor-in-Chief, Far East J Dyn Sys
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114
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Introduction
Mohammad Sajid currently research works in Nonlinear Dynamical Systems, Bifurcation, Fixed points, Chaos and Fractals. He investigates the fixed points, periodic points and their nature as well as draw bifurcation diagrams. To see chaotic behaviour in the system, we use the graphical simulation and numerical computation of Lyapunov exponents. In complex plane, we generate images of the Julia sets (chaotic sets) as fractals. Moreover, we try to apply mathematics in science and engineering.
Current institution
Additional affiliations
August 2005 - present
September 2020 - present
December 2015 - September 2020
Education
July 1996 - July 2004
Publications
Publications (114)
In this paper, a new and generalized contraction principles are proved on complex-valued metric space. By adopting a suitable hypothesis on sequence converging in complex-valued metric space new contractions are established for proving the common fixed-point theorem. Moreover, a rational contractive condition is improved in the complex-valued metri...
The purpose of this article is to provide bifurcation diagrams and observe chaotic behaviour in the real dynamics of two-parameter family of function \(\Phi(x)=x+(1-\lambda x)\ln(ax): x>0, \lambda>0, a>0\). We consider here parameter a is a positive and continuous real parameter while λ is positive but a discrete real parameter. The dynamical prope...
The singular values of two parameter families of entire functions $f_{\lambda,a}(z)=\lambda\frac{e^{az}-1}{z}$, $f_{\lambda,a}(0)=\lambda a$ and meromorphic functions $g_{\lambda,a}(z)=\lambda\frac{z}{e^{az}-1}$, $g_{\lambda,a}(0)=\frac{\lambda}{a}$, $\lambda, a \in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C}$, are investigated. It is shown tha...
In this work, we introduce novel postulates to establish fixed figure theorems with a focus on their extension to the domain of 𝑀_𝑣^𝑏-metric spaces. Consequently, we define conditions ensuring the existence and uniqueness of fixed circles, fixed ellipses, fixed Apollonius circles, fixed Cassini curves, fixed hyperbola, and so on for self mapping. W...
In the present study, a novel version of the contraction theory on a relational partial metric space associated with a binary relation is exhibited. In this process, we observe that numerous relations can be used in many well-known fixed point theorems earlier introduced by multiple authors. We solve an elliptic boundary value problem and an integr...
The study focuses on establishing a fixed point for a class of interpolative contractions by introducing novel forms of interpolative generalized Gupta-Saxena-Reich-type contraction and generalized Gupta-Saxena-Kannan-type contraction within the setting of ${M_v^b}-$metric spaces. We provide non-trivial examples to support the obtained conclusions...
In this study, we have determined the leader-following bipartite consensus conditions for nonlinear singular switched multi-agent systems on non-uniform time domains, using a signed network topology. We present an innovative algorithm based on time scales to effectively address the challenge of structural balance within the signed network.We achiev...
In this paper, we investigate the fractal nature of the local fractional Landau–Ginzburg–Higgs Equation (LFLGHE) describing nonlinear waves with weak scattering in a fractal medium. The main goal of the paper is to introduce and apply the Local Fractional Elzaki Variational Iteration Method (LFEVIM) for solution of LFLGHE. Convergence analysis of L...
This article proposed an image encryption scheme along a novel five-dimensional hyperchaotic system and a Fibonacci Q-matrix (FQ-matrix) for gray images. This designed algorithm follows two key stages: the confusion stage and the diffusion stage. In the confusion step and diffusion step, the placement of the plain image pixels is replaced by a 5D h...
In this article, we explore and analyze the different variants of Julia set patterns for the complex exponential function $W(z) =\alpha e^{z^n}+\beta z^2 + \log{\gamma^t}$ and complex sine function $T(z) =\sin({z^n})+\beta z^2 + \log{\gamma^t}$, where $n\geq 2, \alpha, \beta\in\mathbb{C}, \gamma\in\mathbb{C}\backslash {0}$, and $t\in\mathbb{R}, ~t\...
In developing countries, informal sector is the primary job provider for a significant portion of the workforce. This study aims to analyze how jobs in the informal sector affect the unemployment dynamics of developing nations. To achieve this goal, we formulate a nonlinear mathematical model by categorizing the considered workforce into three dist...
This article dealt with a class of coupled hybrid fractional differential system. It consisted of a mixed type of Caputo and Hilfer fractional derivatives with respect to two different kernel functions, $ \psi_{_1} $ and $ \psi_{_2} $, respectively, in addition to coupled boundary conditions. The existence of the solution of the system was investig...
This paper delves into the investigation of a Volterra-Fredholm integro-differential equation enhanced with Caputo fractional derivatives subject to specific order conditions. The study rigorously establishes the existence of solutions through the application of the Schauder fixed-point theorem. Furthermore, it encompasses neutral Volterra-Fredholm...
The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniquen...
This paper explores the investigation of a Volterra-Fredholm integro-differential equation that incorporates Caputo fractional derivatives and adheres to specific order conditions. The study rigorously establishes both the existence and uniqueness of analytical solutions by applying the Banach principle. Additionally, it presents a unique outcome r...
Much attention have been devoted to control of chaos in nonlinear system in the last few decades and several control procedures have been derived to find the stability target in difference and differential equations. In this study, a novel hybrid chaos control procedure is derived which allows to stabilize the chaos in most accepted discrete chaoti...
Algal blooms pose a significant threat to the ecological integrity and biodiversity in aquatic ecosystems. In lakes, enriched with nutrients, these blooms result in overgrowth of periphyton, leading to biological clogging, oxygen depletion, and ultimately a decline in ecosystem's health and water quality. In this article, we presented a mathematica...
In this study, we establish a new inertial generalized viscosity approximation method and prove that the resulting sequence strongly converges to a common solution of a split generalized mixed equilibrium problem, fixed point problem for a finite family of nonexpansive mappings and hierarchical fixed point problem in real Hilbert spaces. As an appl...
The majority of fractals’ dynamical behavior is determined by escape criteria, which utilize various iterative procedures. In the context of the Julia and Mandelbrot sets, the concept of “escape” is a fundamental principle used to determine whether a point in the complex plane belongs to the set or not. In this article, the fractals of higher impor...
In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the stability of the model’s uniform equilibrium state...
In this article, we prove some common fixed point theorems for generalized rational type contractions in bipolar metric spaces. These theorems also generalize and extend several interesting results of metric fixed point theory to the bipolar metric context. In addition, we provide some examples to illustrate our theorems, and applications are obtai...
In this paper, we primarily investigate the methodology for the hybrid complex projective synchronization (HCPS) scheme in non-identical complex fractional order chaotic systems via an active complex synchronization technique (ACST). Appropriate controllers of a nonlinear type are designed in view of master–slave composition and Lyapunov’s stabilit...
Inspired by the reality that the collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, a circle, an elliptic disc, an ellipse, or a hyperbola, we investigate the subsistence of a fixed point and a common fixed point and study their geometry in a partial metric space by introducing some novel contr...
This work deals with a systematic approach for the investigation of compound difference anti-synchronization (CDAS) scheme among chaotic generalized Lotka-Volterra biological systems (GLVBSs). First, an active control strategy (ACS) of nonlinear type is described which is specifically based on Lyapunov's stability analysis (LSA) and master-slave fr...
![Fig. 1. Border of the Kingdom of Saudi Arabia created using QGIS [54],...](profile/Mohammad-Alresheedi/publication/369490731/figure/fig1/AS:11431281167593939@1686673360071/Border-of-the-Kingdom-of-Saudi-Arabia-created-using-QGIS-54-Pi-version-available-at_Q320.jpg)
Fractal dimension unlike topological dimension is (usually) a non-integer number which measures complexity, roughness, or irregularity of an object with respect to the space in which the set lies. It is used to characterize highly irregular objects in nature containing statistical self-similarity such as mountains, snowflakes, clouds, coastlines, b...
We present convergence and common fixed point conclusions of the Krasnosel'skii iteration which is one of the iterative methods associated with α-Krasnosel'skii mappings satisfying condition (E). Our conclusions extend, generalize and improve numerous conclusions existing in the literature. Examples are given to support our results.
In this manuscript, we explore stunning fractals as Julia and Mandelbrot sets of complex-valued cosine functions by establishing the escape radii via a four-step iteration scheme extended with s-convexity. We furnish some illustrations to determine the alteration in generated graphical images and study the consequences of underlying parameters on t...
In this paper, we prove some common fixed point theorems for generalized rational type contraction in bipolar metric spaces. These theorems also generalize and extend several interesting results of metric fixed point theory to the bipolar metric context. In addition, there are some examples and applications for the obtained results.
2020 Mathematic...
Completed 100 reviewed papers as reviewer for MDPI journals
In this paper, the dual combination–combination hybrid synchronization (DCCHS) scheme has been investigated in fractional-order chaotic systems with a distinct dimension applying a scaling matrix. The formulations for the active control have been analyzed numerically using Lyapunov’s stability analysis in order to achieve the proposed DCCHS among t...
In this article, we will investigate a retarded van der Pol-Duffing oscillator with multiple delays. At first, we will find conditions for which Bogdanov-Takens (B-T) bifurcation occur around the trivial equilibrium of the proposed system. The center manifold theory has been used to extract second order normal form of the B-T bifurcation. After tha...
In this paper, we present some results of coupled fixed points for the system of non-linear integral equations in Banach space. Our results enlarge the results of newer papers. Additionally, we prove the applicability of those results to the solvability of the system of non-linear integral equations. Finally, we give an example to validate the appl...
Here we will investigate a retarded damped oscillator with double delays. We looked at the combined effect of retarded delay and feedback delay and found that the retarded delay plays a significant role in controlling the oscillation of the proposed system. Only the negative damping situation is considered in this research. At first, we will find c...
In this article, we use the tool of monotone nonlinearity to present the approximate controllability discussion for fractional semilinear system with nonlocal conditions. Monotonicity is an important characteristic in many communications applications in which digital-to-analog converter circuits are used. Such applications can function in the prese...
The paper deals with numerical analysis of solutions for state variables of a CoVID-19 model in integer and fractional order. The solution analysis for the fractional order model is done by the new generalized Caputo-type fractional derivative and Predictor-Corrector methodology, and that for the integer order model is carried out by Multi-step Dif...
One of the key factors to control the spread of any infectious disease is the health care facilities, especially the number of hospital beds. To assess the impact of number of hospital beds and control of an emerged infectious disease, we have formulated a mathematical model by considering population (susceptible, infected, hospitalized) and newly...
In this research, we look at the Julia set patterns that are linked to the entire transcendental
function f (z) = ae^z^n+ bz + c, where a, b, c ∈C and n ≥ 2, using the Mann iterative scheme,
and discuss their dynamical behavior. The sophisticated orbit structure of this function, whose
Julia set encompasses the entire complex plane, is described us...
Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object in nature. Many fractals may repeat their geometry at smaller or larger scales. This paper is the second (and last) part of a series of two papers dedicated to an eclectic survey of fractals describing the infinite complexity...
In this article, a Leslie-Gower type predator prey model with fear effect has been proposed and studied in the framework of fractional calculus in Caputo sense. The well-posedness of the system has been verified analytically. The states of stability of the possible non-negative equilibrium points have been derived. It is observed that both the fear...
This paper presents the self-tuned Automatic Generation Control for an interconnected power system with dominant wind energy penetration. The uncertain behavior of wind power plant has random fluctuations on the frequency of the power system and optimum performance cannot be achieved by the fixed structure controller. Thus, the self-tuned controlle...
In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka–Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapunov stability theory (LST) to construct the desired controllers, which ensures the global asymptotical conve...
Inthispaper,wegeneratesomenon-classicalvariantsofJuliaandMandelbrotsets,utilizing the Jungck-Ishikawa fixed point iteration system equipped with s-convexity. We establish a novel escape criterion for complex polynomials of a higher degree of the form zn + az2 − bz + c, where a, b, and c are complex numbers and furnish some graphical illustrations o...
The outcome of heat sink/source on natural convection movement with temperature andMagnetohydrodynamics transport from a vertical cone with variable surface heat fluxis discussed. The leading boundary layer equation are obtained to dimensionlessequation of the movement are explained by an absolutely stable finite difference systemof Crank-Nicholson...
Fractals are geometric shapes and patterns that may repeat their geometry at smaller or larger scales. It is well established that fractals can describe shapes and surfaces that cannot be represented by the classical Euclidean geometry. An eclectic survey of fractals is presented in two parts encompassing applications of fractals in a variety of di...
In this paper, the recent trends of CoVID-19 infection spread have been studied to explore the advantages of leaky vaccination dynamics in SEVR (Susceptible Effected Vaccinated Recovered) compartmental model with the help of Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in the Caputo sense (ABC) non-singular kernel fractional derivative oper...
This paper presents hybrid model predictive control-based automatic generation regulator design for dominant wind energy penetrated multisource power system. The other power generation sources hydro and thermal are also considered in each area. The proposed AGC regulator is designed for each independent area considering only local power system stat...
In this article, we present some recent advances in the dynamics of one variable complex functions which are especially associated to the Julia sets, the Fatou sets, the Sigel disks, the Herman rings, fixed points as well as the Mandelbrot sets. For the sake of interest, we consider mainly research works which have been done from 2015 to 2019. To a...
In this manuscript, a methodology is designed to investigate the microscopic chaos adaptive controlling in the dynamics of the chaotic chemical reactor system (CR-system) using hybrid projective synchronization (HPS) technique. Initially, an adaptive control design (ACD) has been presented and analyzed in a systematic manner for controlling the mic...
We explore some new variants of the Julia set by developing the escape criteria for a function sin(zn ) + az + c, where a, c ∈ C, n ≥ 2, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these f...
MDPI is a publisher of open access, international, academic journals. We rely on active researchers, highly qualified in their field to provide review reports and support the editorial process. The criteria for selection of reviewers include: holding a doctoral degree or having an equivalent amount of research experience; a national or internationa...
The main concern of this manuscript is to examine some sufficient conditions under which the fractional order fuzzy delay differential system with the non-instantaneous impulsive condition has a unique solution. We also study the existence of a global solution for the considered system. Fuzzy set theory, Banach fixed point theorem and Non-linear fu...
Fractal dimension measures the degree of geometric irregularity present in the objects. The divider method and the box-counting method are two classical approaches for computing fractal dimension of natural objects and other fractals. In this article we calculate the fractal dimension of border of India and coastline of India using a novel multicor...
Agriculture is the main source of income for most of the people from thousands of years but still every year farmers suffer loss of crop and money, due to misinterpretation of soil or climatic conditions. In the recent years, researchers have worked to improve this state and agriculture for production of crop by analyzing soil or climate conditions...
http://www.pphmj.com/journals/fjds_editorial_board.htm
The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID‑19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transm...
This paper discusses the oscillation of nonlinear even-order differential equations with mixed nonlinear neutral terms. We establish new oscillation criteria, which extend, improve, and simplify existing criteria given in the literature. For illustration, some examples are provided.
In this work, we investigate the controllability of singular dynamic systems on time scales. First, we decompose the consider systems into a slow subsystem and a fast subsystem. After that, we use the Laplace transform and convolution theorem to derive the state response of these two subsystems. Finally, we established some necessary and sufficient...
The intention of this exertion is to inspect the flow heat and mass transfer of unsteady magnetite Casson nanofluid over a wedge. The peak theme of thermal radiation and chemical reaction are also incorporated. Slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. The governing equations are tr...
This paper is devoted to a hierarchical approach of constructing a class of fractal interpolants with trigonometric basis functions and to preserve the geometric behavior of given univariate data set by these fractal interpolants. In this paper, we propose a new family of -rational cubic trigonometric fractal interpolation functions (RCTFIFs) that...
A modified version of our previously analyzed prey-predator refuge model is presented in this article by introducing Allee effect on the predator species and mutual interference among the predators. Possible number of coexistence equilibrium points are investigated with the help of prey and predator nullcline. The local stability and Hopf-bifurcati...
Coastlines are irregular in nature having (random) fractal geometry and are formed by various natural activities. Fractal dimension is a measure of degree of geometric irregularity present in the coastline. A novel multicore parallel processing algorithm is presented to calculate the fractal dimension of coastline of Australia. The reliability of t...
Background:
Human health issues caused by cigarette smoke carcinogens (CSC) are increasing rapidly every day and challenging the scientific community to provide a better understanding in order to avoid impact on communities. Cigarette smoke also contains tobacco-based chemical compounds harmful to human beings either smokers or non-smokers.
Objecti...
In this article, a non-linear mathematical model has been proposed by incorporating the influential non-medicinal prevention measures together with an optimal control strategy to minimize the intervention cost of COVID-19 outbreak in India. During the unavailability of prescribed vaccines or antivirals, the transmission of COVID-19 infection has tr...
This study presents the chaotic oscillation of the satellite around the Earth due to aerodynamic torque. The orbital plane of the satellite concurs is same as the tropical plane of Earth. The half-width of riotous separatrix is assessed utilizing Chirikov’s measure. Variety of boundary techniques shows that streamlined force boundary (ɛ), unpredict...
https://www.mdpi.com/2227-7390/9/2/196/htm
In this paper, we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus (COVID-19). The model incorporates the effect of transmission and treatment on the occurrence of new infections. For the model, the basic reproduction number [Formula: see text] has been computed. Corresponding to the threshold quantit...
In this research article, the development of Fe-35Mn-5Cu alloy (bio-degradable) through mechanical alloying was discussed. The two key important parameters in mechanical alloying process, namely, milling time (1 and 10 h) and ball-to-powder ratio, BPR (5:1 and 15:1) were taken as variable input parameters. The other parameter of milling speedwas se...
This article is devoted to investigate the singular values as well as the real fixed points of one-parameter families of transcendental meromorphic functions which are associated with fundamental trigonometric functions $\sin z$, $\cos z$ and $\tan z$. For this purpose, we consider the functions $f_{\mu}(z)=\mathlarger{\frac{\sin z}{z^{2}+\mu}}$, $...
This article is devoted to the study of chaos and bifurcation in the real dynamics of a newly proposed two-parameter family of transcendental functions. We assume that one parameter is continuous and other parameter is discrete. For certain parameters, the theoretical computations of the real fixed points of a family of functions are given. The num...
The focus of this research work is to obtain the chaotic behaviour and bifurcation in the real dynamics of a newly proposed family of functions f λ , a x = x + 1 − λ x ln a x ; x > 0 , depending on two parameters in one dimension, where assume that λ is a continuous positive real parameter and a is a discrete positive real parameter. This proposed...
The work aimed in this paper is to develop an effective integrated load forecasting technique using the real time data based on energy consumption for minute to-minute, hourly, daily, monthly and yearly at substation level. The various techniques like time series, fuzzy, artificial neural network, wavelet and hybrid time series methodologies are im...
: This research work is focused to develop and investigate the mathematical linear and non-linear modelling techniques for mechanically alloyed nanocomposites materials. These conventional and non-conventional artificial intelligent models could predict the both physical and mechanical properties of some nanocomposites materials. The conventional t...
Our main objective is to study the real fixed points and singular values of a two-parameter family of transcendental meromorphic functions $g_{\lambda,n}(z)=\lambda \frac{z}{(b^{z}-1)^{n}}$, $\lambda \in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C} \backslash \{0\}$, $n\in \mathbb{N} \backslash \{1\}$, $b>0$, $b\neq 1$ in the present paper which...
Chaotic behaviour in the real dynamics and singular values of a two-parameter family of generalized generating function of Apostol-Genocchi numbers, $f_{\lambda,a}(z)=\lambda \frac{2z}{e^{az}+1}$,
$\lambda, a\in \mathbb{R} \backslash \{0\}$, are investigated. The real fixed points of $f_{\lambda,a}(z)$ and their nature are studied. It is seen that...
The main goal of the present paper is to investigate the singular values of three-parameter families of transcendental (i) entire functions $f_{\lambda,a,\mu}(z)=\lambda\bigg(\dfrac{e^{az}-1}{z}\bigg)^{\mu}$ and $f_{\lambda,a,\mu}(0)=\lambda a^{\mu}$; $\mu> 0$, $\lambda, a\in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C}$ (ii) meromorphic functio...
The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions f λ , n ( x ) = λ x ( e x + 1 ) n , λ > 0 , x ∈ R , n ∈ N \ { 1 } which arises from the generating function of the generalized Apostol-type polynomials. The existence of the real fixed points of f λ , n ( x ) and the...
The singular values of two kinds of two-parameter families of functions (i) f_λ,μ(z)=λ((b^z−1)/z)^μ and f_λ,μ(0)=λ(lnb)μ, μ>0, (ii) g_λ,η(z)=λ(z/(b^z−1))^η and g_λ,η(0)=λ(lnb)η, η>0; λ∈ℝ∖{0}, z∈ℂ, b>0, b≠1 are described. It is shown that all the critical values of fλ,μ(z) and gλ,η(z) lie interior and exterior of the disk centered at origin and havi...
The singular values of two-parameter families of functions arising from Apostol-Genocchi polynomials of higher order are investigated. For this purpose, we consider the functions f_λ,µ (z) = λ((e^z +1)/ 2z)^ µ , µ > 0, z ∈ C\{0} and g_λ,η (z) = λ(2z/(e^z +1))^η , η > 0, z ∈ C; λ ∈ R\{0} in this paper. It is shown that the functions f_λ,µ (z) and g_...
The two-parameter family of f_{\lambda,n}(z)=\lambda \frac{z}{(e^{z}-1)^{n}}, \lambda \in \mathbb{R} \backslash \{0\}, z \in \mathbb{C} \backslash \{0\}, n\in \mathbb{N} \backslash \{1\}, is considered in this paper. The existence and nature of the real fixed points of f_{\lambda,n}(x), x\in {\mathbb{R}}\setminus \{0\} are described for n odd and n...
The characterization and properties of Julia sets of one parameter family of
transcendental meromorphic functions $\zeta_\lambda(z)=\lambda \frac{z}{z+1}
e^{-z}$, $\lambda >0$, $z\in \mathbb{C}$ is investigated in the present paper.
It is found that bifurcations in the dynamics of $\zeta_\lambda(x)$, $x\in
{\mathbb{R}}\setminus \{-1\}$, occur at se...
In this paper, the real fixed points and dynamics of one parameter family of functions fλ(x)=λf(x),λ>0, where f(x)=(b^x-1)/x,x≠0 and f(0)=lnb for b>0,b≠1, are investigated. The real fixed points of fλ(x) as well as their nature are explored. For 0<b<1, it is seen that one fixed point of fλ(x) is attracting and one fixed point is repelling for 0<λ<λ...
The singular values of one parameter family of functions $f_{\lambda}(z)=\lambda \frac{e^{z}+1}{2z}$,
$\lambda\in \mathbb{R} \backslash \{0\}$, $z\in \mathbb{C} \backslash \{0\}$, are studied. It is shown that the function $f_{\lambda}(z)$ has infinitely many singular values. The critical values of $f_{\lambda}(z)$ lie exterior of the open disk, th...
The purpose of the present work is to study the chaotic behavior in a flexible assembly line of a manufacturing system. A flexible assembly line can accommodate a variety of product types. Result analysis is performed to obtain time persistent data. The behavior of the system is observed for Work-In-Process, as assembling systems are sensitive duri...
The goal of this paper is to describe the singular values of one parameter family of generalized generating function of Bernoulli's numbers, $f_\lambda(z)=\lambda \frac{z}{b^{z}-1}$, $f_{\lambda}(0)=\frac{\lambda}{\ln b}$ for $\lambda \in \mathbb{R} \backslash \{0\}$, $z \in {\mathbb{C}}$ and $b>0$ except $b=1$. It is found that the function $f_{\l...
The singular values of one parameter family of entire functions $f_{\lambda}(z)=\lambda\dfrac{b^{z}-1}{z}$ and $f_{\lambda}(0)=\lambda\ln b$, $\lambda\in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C}$, $b>0$, $b\neq 1$ is investigated. It is shown that all the critical values of $f_{\lambda}(z)$ lie in the right half plane for $0<b<1$ and lie in...
Singular values and fixed points of one parameter family of generating function of Bernoulli's numbers, $g_\lambda(z)=\lambda \frac{z}{e^{z}-1}$, $\lambda \in \mathbb{R} \backslash \{0\}$, are investigated. It is shown that the function $g_{\lambda}(z)$ has infinitely many singular values and its critical values lie outside the open disk centered a...
In the present paper, the singular values of one parameter family of entire functions $f_{\lambda}(z)=\lambda\bigg(\dfrac{e^{z}-1}{z}\bigg)^{m}$ and $f_{\lambda}(0)=\lambda$, $m\in \mathbb{N}\backslash \{0\}$, $\lambda\in \mathbb{R} \backslash \{0\}$, $z \in \mathbb{C}$ is investigated. It is shown that all the critical values of $f_{\lambda}(z)$ l...
In the present paper, the real fixed points of one parameter family (Formula presented.) and (Formula presented.) are investigated. Further, the nature of these fixed points of fλ(x) are shown for b > 0 except b = 1.
The chaotic behavior in the real dynamics of a one parameter family of nonlinear functions is studied in the present paper. The fixed points, periodic points and their nature are investigated for the functions considered in this study. Bifurcation, and period doubling, which is a route of chaos in the real dynamics, are also shown to take place in...
The purpose of this paper is to study the singular values and real fixed points of one parameter family of function, $f_\lambda(z)=\lambda \frac{z\,b^{z}}{b^{z}-1}$, $f_{\lambda}(0)=\frac{\lambda}{\ln b}$ for
$\lambda \in \mathbb{R} \backslash \{0\}$, $z \in {\mathbb{\hat{C}}}$ and $b>0$ except $b=1$. It is found that the function $f_{\lambda}(z)$...
The singular values of the one parameter family of singular perturbed
exponential map $f_{\mu}(z)=e^{z}+\frac{\mu}{z}$, $\mu$ is non-zero real, are investigated. It is found that the function $f_{\mu}(z)$ has infinitely many singular values and all these singular values are bounded.
Questions
Questions (2)
Now, in continuation of my previous question about spreading of Coronavirus:
Currently, exposing of Coronavirus in India like fractal branching and now chaotic burst has been happened. It is somehow depends on several huge gatherings on some occasions in India from early 2021 to till April 2021. Many of them saying, peak of it about mid May but prediction is very difficult since it is chaotic situation. Saying about peak, it is very uncertain since graph of coronavirus in India is growing unpredictable way. I observe that peak of it in India after June.
